Interacting Particle Systems and Their Scaling Limits.

1996 ◽  
Author(s):  
S. R. Varadhan
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Scaling Limits ◽  
Interacting Particle

Diffusive Scaling Limits of Mutually Interacting Particle Systems

2004 ◽  
Vol 35 (6) ◽  
pp. 1512-1533
Author(s):  
Shui Feng ◽  
Ilie Grigorescu ◽  
Jeremy Quastel
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Scaling Limits ◽  
Interacting Particle

scholarly journals Condensation of SIP Particles and Sticky Brownian Motion

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Mario Ayala ◽  
Gioia Carinci ◽  
Frank Redig
Keyword(s):  
Brownian Motion ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Self Duality ◽  
Inclusion Process ◽  
Interacting Particle ◽  
New Information ◽  
Homogeneous Product ◽  
Coarsening Dynamics ◽  
The Difference

AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.

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